The following is an article that should help convince the reader that there are waves in Dark Matter.

Dark Matter Waves and Planetary Rings
Orvin E.Wagner

ABSTRACT

In the late 1980’s I discovered low velocity, matter penetrating waves that suggest that dark matter is their medium. Since then, others and I have found that dark matter must be denser on earth and in the solar system than most have previously surmised. A solution to a wave equation suggests that the planets of the sun and the satellites of planets were placed at standing wave nodes produced by low velocity waves from the sun due to dark matter oscillating in the sun. The oscillating of the sun, indicated by the solar cycle, and similar oscillation of the gaseous planets are apparently dark matter phenomena. The velocity of the produced standing waves is proportional to the reciprocal of the square root of the density of the dark matter medium with the velocity of the waves increasing linearly from the sun at least out to 10¹⁰ km. The solution to the wave equation provides history of the solar system, details of the structure of the gaseous planets, explains stable rings as produced by ongoing oscillations of planetary layers, and much more. Apparently dark matter does more than just keeping the galaxy together as most have surmised. The solar system and other star systems are apparently stabilized and organized by dark matter waves. The same waves likely also stabilize and organize larger structures in the universe. They may also produce the rings of the gaseous planets, which this paper discusses, as well as explain variable stars and so on. My explanations are supported by their simplicity and thus supported by Occam’s razor.

INTRODUCTION

In my early work with plants and other media I found wave characteristics that seem to support some unknown wave medium. Plants seem to oscillate with low velocity standing waves. I observed low velocity sound like signals moving between and within plants (Wagner 1989) and lately between plants and shielded artificial transmitters (Wagner 2008,2010). Since the signals are very low velocity and seem to penetrate everything I hypothesized early that the predominate medium is dark matter combined with other matter such as air, plant tissue, metal shields, and any other kind of matter. I carried my ideas to the solar system and beyond. Dark matter is hypothesized to be associated with stabilizing and organizing the solar system, which includes planets, planetary satellites and rings around planets (Wagner 1999). If one considers that the dark matter density drops of as 1/r² going away from the sun and it’s density is suggested to be 0.3 Gev/cm³ beyond Neptune (10¹⁰ Km from the sun) then the density at Neptune without Neptune present is 1.48 Gev/cm³ (2.38x 10^-10 joules/cm³) and on the earth’s surface is near 1.5x10⁵ Gev/cm³ (Wagner 2010) . The idea that dark matter is influencing local phenomena may seem fantastic but it only makes sense. There is much argument about the local density of dark matter but my results, if my hypotheses are correct, indicate that the density and the resulting effects are large. I assume that the velocity of dark matter waves is proportional to the reciprocal of the square root of the dark matter density and it increases in density from 10¹⁰ km (at about 0.3 Gev/cm³, an early estimate found in the literature) to the sun. The velocity is found to be 1.25 m/s at the sun’s surface then the velocity at 10¹⁰ km is 17,986 m/s. The 1.25 m/s was derived in my 1999 paper (Wagner 1999a). 17,986 m/s agrees with my derived velocity v=1.25r/r₀ where r₀ is the sun’s radius and r is 10¹⁰ km. Everything seems to agree with the wave hypothesis as additionally worked out below. Note that many individuals are skeptical of dark matter playing such a local role as I present here and think that gravity is the only influence. Planetary rings, however, often are sharply defined. This suggests that they are being produced by something sharply resonant (with high Q as described in electronics). This would not be true for rings purely gravity controlled. In this article I present approximate wave solutions to planetary rings.

DARK MATTER WAVES ON EARTH

In my experiments with plants for the past many years, I have assumed that the penetrating waves I discovered in plants are dark matter waves. The waves in plants seem to have larger velocities vertically than horizontally with an increase in velocity to the vertical. The differences may indicate something as to how dark matter interacts with gravity. Plants appear to be shaped by the difference in velocities at different angles (Wagner 2008 and much earlier). This should perhaps tell us something more about gravity’s relation to dark matter. So far the most common velocity in air appears to be near 25 m/s for the horizontal velocity. The 25 m/s was found from correcting the 1988 measured velocity (Wagner 1989) and lately velocity measurements made from oscillation between trees and salt filled shielded samples and between shielded samples (Wagner 2009). It is possible that there is a spread in velocities since some of the received curves seem to indicate very high velocities down to 25m/s at maximum amplitude and to lower amplitudes with lower velocities on the opposite side of the distribution curve. On May 8, 2009 I was comparing the amplitude of signals being sent from the lab to the residence (about 54 m). I used the usual samples in metal boxes comparing the signal strengths of signals from horizontal samples and vertical samples. The amplitudes of signals between vertical samples were more than twice the amplitude of signals between horizontal samples. The noise amplitude from the vertical receiving sample was more than twice the amplitude of the sample when it was horizontal. The data indicates that the noise is coming from outside of the sample and is probably caused largely by dark matter particles. This may indicate that 1/f noise is caused by dark matter particles (Wagner 2008).

THE OSCILLATING SUN AS A WAVE SOURCE

The sun and other stars apparently oscillate with dark matter waves. There may be resonant sizes of stars so forming stars blow off matter. An oscillating excessive matter layer may explain variable stars. The sun emits waves into the surrounding dark matter that reflect back on themselves to produce nodes as equation (1) below suggests. The nodes from the sun are where planets apparently formed from the original pre-planetary nebula. The same appears to be true for satellites of gaseous (and also oscillating) planets. The waves increase in velocity with distance from the sun (the wave velocity is proportional to the reciprocal of the square root of the dark matter density). The dark matter density becomes smaller and the planets’ spacings increase, as observed, and as described by equation (1) below. Equation 1 describes their locations very closely, starting with N=7 for Mercury, except for earth and Pluto which likely were influenced by special conditions present at formation and placement. Apparently earth takes the place of two planets setting between their possible locations (Wagner 1999a).

The radius of the sun in meters is the magnitude of 22.2 years in seconds! 22.2 years in seconds is the period of the solar cycle! The frequency of oscillation is just the magnitude of 1/r₀ in the sun. I suggest above that other stars have resonant sizes. Oscillating stars produce standing waves in the surrounding dark matter and nodes going away from the star may tend to be locations where planets form in pre-planetary matter. The observed wave velocities correlate with slow moving particles, which may be characteristic of cold dark matter, WIMPS, perhaps.

Dark matter seems to move charge in the sun as apparently it does in my experiments but the temperature doesn’t seem to change the wave velocity. Temperature seems to have little effect on the oscillating waves in the sun apparently providing an expected characteristic of dark matter. It interacts little electromagnetically. Here is a description of the solar cycle that I wrote as an abstract for a meeting of the Northwest Section of the American Physical Society in 2000:

“ In Physics Essays 12:3-10 I explain the placement of the planets in terms of low velocity waves emitted by the sun. The initial high latitude sunspots observed on the butterfly diagram indicate evidence for a wave pulse generated near the center of the sun. The wave pulse carries charge with it as is observed for similar waves in plants (W-waves). For the first half cycle negative charge is carried to the surface of the sun where much of the wave pulse radiates a wave crest into space while the charge slowly redistributes itself over in within the sun. This charge redistribution is probably a relatively slow process in the turbulent sun. Meanwhile the next wave pulse carrying positive charge moves outward. Charge rotating with the sun determines the polarity of the sun’s magnetic poles so they reverse as the pulse moves outward. The wave pulse, which interacts strongly with force fields, is guided by centripetal force and gravity so that the pulse radiates outward into space near the sun’s equator. W-waves produce an automatic return wave in the vacuum (dark matter) so that standing waves are produced in the space around the sun providing a template for the formation and stabilization of planets in orbit. The solar cycle provides another evidence that W-waves provide for self organization for both the universe and life”. (W-waves comes from my original wood waves)

In my article Waves in Dark Matter published in Physics Essays in 1999 I derive an expression from a wave equation. This expression does a great job locating the planets of the sun, locating the satellites of the planets, providing history etc. The results are very gratifying, reasonable, and simple:

(1) r=r₀exp(0.625N)

N is an integer starting with N=7 for Mercury as a sun’s planet. r is the distance to the planet or satellite of a gaseous planet, r₀ is the radius of the sun or planet (or a previous radius when working with early radii). The fit is not perfect but is excellent.

Note that the reciprocal of 0.625 is 1.6, for those who consider 1.6 a special number. Equation (1) is apparently very good at deriving the history of a planet because it seems to provide details on how a planet, its satellites, and rings were formed assuming wave formation. Apparently planets were often smaller in radius when satellites were placed. Applying equation (1), the satellites often seem to tell us something of the history of the buildup of the planet. In some cases it appears that some satellites were placed when the radius was larger, like Saturn may have been hotter at one time and it thus had a larger radius than it has now. Or the sun was somewhat larger when planets were placed using equation (1). Many satellites indicate that the associated planet was smaller when they were placed using equation (1). Stable rings seem to be held in place in an ongoing manner by oscillating planetary layers and don’t often need shepherd moons. Satellites, however, apparently are subject to being displaced by outside forces such as collisions and increasing gravity as matter is added to a planet or satellite. Much of the important work seems to come out of using N=1 in equation 1 especially for determining early planetary radii. The simple equation seems to be very versatile in its application and the equation demonstrates that waves are involved. The equation is derived from a wave equation (Wagner 1999). To derive the velocity dr/dt from (1) remember that dN/dt is just 2N/period. The period is just the magnitude of r₀ (meters) in seconds for the sun. Thus v is just v=v₀exp (0.625N) for the sun where v₀ is 1.25 m/s for the velocity perpendicular to the sun’s surface at the surface. Or v=v₀r/r₀ for dark matter waves leaving the sun with standing wave nodes accounting for the separation of the planets.

The oscillating frequency of the sun can be written as 1.19/(r₀Ö d). 1.19 is the square root of the sun’s relative mean density. r₀ is the radius and d is the relative mean density. Here one must recall that often in physics, with sound for example, the wave velocity is proportional to the reciprocal to the square root of the density of the medium. If the denominator contains the sun’s mean density the frequency of the sun’s oscillation is just 1/r₀ or 22.2 years is the period. The magnitude of 22.2 years in seconds (the apparent solar cycle period) is just equal to the sun’s radius in meters. The mean velocity of the waves causing the solar cycle is thus apparently close to 1 m/s. 1 m/s is also close to the sun’s surface wave vertical velocity (1.25 m/s) that I found first in my 1999 Physics Essays article. Other star’s frequencies apparently are 1/radius (or 1/layer thickness for oscillating layers in planets) corrected by possible different wave velocities.

We will assume that dark matter behaves like a special gas. It starts out to be a low rms velocity gas with wave propagation velocities on the earth’s surface in air around 25 m/s (measured horizontal velocity (Wagner 1989, 2009) and on the sun’s surface about 1.25 m/s and within the sun around 1.0 m/s. In my early work I found that the wave velocities apparently have something to do with gravity direction as well as other environmental factors (Wagner 2007). This is why I give the measured surface of the earth velocity as horizontal. Looking at the formulas indicates that dark matter does behave like a gas in the gaseous sun since the velocity appears to be proportional to the reciprocal of the square root of the mean density of the sun, which includes dark matter.

In Wagner 1999 the density of dark matter is given as:

(2) d=C/r² from the sun

The velocity of dark matter waves is proportional to the reciprocal of the square root of the density of dark matter thus v=a constant times r using eq. 2. This concurs with the equation for the velocity of sound like dark matter waves going away from the sun derived in Wagner 1999 as v=v₀r/r₀. We can use this relation to find an approximate density of dark matter on the earth’s surface. I calculate the density of dark matter on the surface of the sun as 9.97 x 10^-3 joules/cm³ using the idea that the density of dark matter drops off as 1/r² from the sun’s center and using the density as 0.3 Gev/cm³ (an early estimate found in the literature) at 10¹⁰ km from the sun. Using 1.25 m/s as the sun’s surface wave velocity and 0.3 Gev/cm³ at 10¹⁰ km and 2500 cm/s for the wave velocity found in recent work (Wagner 2010) on the earth’s surface gives 1.56x 10⁵ Gev/cm³ for the dark matter density on the earth’s surface. In both cases I am depending on the value of 0.3 Gev/cm³ at 10¹⁰ km. A recent reference (2008) giving an order of magnitude calculation of the dark matter density on the earth’s surface of 10⁵ Gev/cm³ fits very well (Frere et. al. 2008)). I attempted to find the density of dark matter on the surface of planets by assuming densities a certain distance from the planets from the density of dark matter at 10¹⁰ km. from the sun.So far I didn’t come up with reasonable answers apparently because planets collect their individual balls of dark matter independent from the sun.

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INTERPETING THE RINGS OF THE GASSEOUS PLANETS

First I discuss some general principles. We apparently can often use equation (1) to find the locations of the layers of a planet. We assume that most often rings are being maintained by ongoing oscillations of planetary layers so they provide accurate present information. Stable rings apparently don’t need shepherd moons. Rings may form and then quickly dissipate unless there is something to hold them in place. I usually have neglected to take into account some tiny satellites. The locations of substantial satellites, especially the close in ones, should provide us information on original radii and layer thicknesses of planets by equation (1). The problems with satellites are that they likely have moved from their initial locations due to random collisions and orbit changes due to added matteron the parent planet. With the gaseous planets and others it is often apparent that satellites were added during buildup of the planet. The buildup will change results when using present satellite locations in attempting to calculate original radii. I am not sure of the densities and compositions of the planetary layers so I will approximate wave velocities in a layer by assuming 1-2 m/s as in the sun for 1 m/s but likely the velocity is larger than 1 m/s as a function of the composition. In general it appears that deep rings are due to a layer with a gradient in composition that generates a continuum of frequencies. The signals outside the planet produce rings that appear as one deep ring because they are produced by signals that are close together in frequency. In my calculations here I will assume the latter. I can thus consider a wide ring using only its distance farthest from the planet in calculations since that will provide the total thickness of the planetary layer. Very thin layers oscillating alone would produce high frequency signals producing rings too close to the planet to show. The rings and satellites permit one to obtain a very good idea of the radius of the rocky core. One thing that helps, in calculations, is that satellite orbits that were added, after layers were placed on the rocky core are not disturbed as much because the added layers are likely less dense than the rocky core. One important item I want to point out is that if a planet only has a few rings like Neptune it is likely only a portion of the material above the rocky core is oscillating. With Uranus the rings are so continuous most of planet is likely oscillating.

The placement equation (r=r₀exp(.625N)) seems to hold even when planets were larger or smaller when the satellites were placed and thus may provide much history as stated earlier. If light matter is added after a satellite is placed the satellites location may not change much. Many events, however, occurred that often modified the locations of planets and their satellites. Also as pointed out in my 1999 article radii of the sun and planets were different at different times due to temperatures of the gaseous planets and loss of radius by the sun due to loss of matter. For this reason a larger radius for the sun is presented in the original article (Wagner 1999). The satellite placement rule presented here probably becomes less effective at the largest values of N, which is to be expected with a near perfect fit for Mercury and Venus for the sun. Also cataclysmic events and different initial conditions likely changed locations of planets and satellites.

Others have suggested layers in the gaseous planets (See nasa.gov). Equation (1) suggests outer layers when we apply it to close in satellites of planets like Neptune. Analyzing the rings and satellites of gaseous planets suggest that gaseous planets have gaseous outer layers. A layer is assumed to often oscillate putting out a standing wave whose second node is at the location of a ring with the first (forced) node at the surface of the planet. The frequency producing a ring is determined here to be equal to the average velocity of the wave from the planet’s surface to the ring divided by twice the distance from the planet’s surface to the ring since the distance involved is half a wavelength. The oscillations producing rings are usually only considered strong enough to produce rings at first outer nodes. I early suggested that rings form where there is only one resonance while satellites form where the length of the orbit is an integral multiple of wavelengths as well as a resonant radius being present, in other words perhaps at a double node (Wagner 1999).

Calculations for JUPITER

This history is derived using equation (1). The closest two satellites give us an early radius of approximately 30,500 km. A third satellite gives us an N=2 satellite at 109,800 km during the early period. The early radius is probably close to the radius of the rocky core. Then gaseous type material was added which heated to a high temperature to bring the radius to 80,500 km when 5 satellites were added at first 150,408 km away from the planets surface, then at 281,000; 504,393; 980,788; and 1,832,354 km. The actual present distances of the latter are 150,408; 350,108; 541,908; 998,508 and 1,811, 508 km. Apparently the satellites have been knocked around a little and the equation doesn’t account for changes in orbits due to added mass. The radius is now 71,492 km. after cooling. I use distances from the planets surface since equation (1) starts at r₀. Since I assume that rings are usually produced by ongoing oscillation, I estimate that there is a 40,983 km set of layers on top of the rocky core. The question is how much of this is oscillating to produce the rings. For thick rings I assume that they are produced by one thick layer with a gradient in composition. The lowest frequencies would be expected to produce the farthest out nodes and the lowest frequency produced by the full thickness of the oscillating layer within the planet. A frequency would be given by the average velocity out to the ring from the planet surface divided by twice the radius of the ring minus the planetary radius or ((v +v₀)/2)/2(r-r₀). We can write an very approximate expression for the period of oscillation for a planetary ring as 2(r_n-r₀)/s (1+r_n/r₀)/2=4(r_n-r₀)/s (1+r_n/r₀ ) where s is the surface velocity and r_n is the distance from the planet surface to the ring. In Wagner 1999 the velocity of dark matter wave going away from a wave source increases linearly. The distance to the ring node is a half wavelength. Since we do not know the compositions of the layers we can start by summing the periods of all the dominant rings and not held in place by shepherd moons, and set the sum equal to the thickness of the total active layer assuming it oscillates with a total period equal to the magnitude of the thickness in meters! Use avalue twice this thickness for a total period. This should give us some idea of the average velocity out to the rings from the planets surface even though the period of the layer oscillations is very approximate. Using the calculated surface velocity we may be able to arrive at some idea of the density of dark matter above the planets surface. The mean distance from the surface to the rings is 115,553 km (suggesting thick low frequency layers within the planet).
∑_n1/f_n=∑2(r_n-r₀)/s((1+r_n/r₀)/2)=p_t =(2(51508)/(1.720)/2))+2(57488)/((1.804)/2)+2(109858)/((2.537)/2)+2(150402)/((3.104)/2)+2(208508)/(3.917/2))/s=40992 for Jupiter (or 2 x40992)

Thus s=20.18m/s for the surface wave velocity. The surface gravity here is 2.34 times the earth’s surface gravity and the surface density of dark matter should be high accordingly and thus the surface velocity may be close to half the 20.18 or 10.09 m/s for twice 40992. Doubling 40992 provides for a full period of layer oscillation.

The rings extend far into space so one might expect a high average velocity out to the rings, which can be easily calculated using the surface velocity. Note that the mass of Jupiter is 318 times that of earth and its density is 1.3 suggesting that even though it is further from the sun the density of dark matter around it appears to be large since the planets appear to collect their own dark matter mostly independently of the sun.

If one compares the ring systems of Jupiter, Saturn, Uranus, and Neptune one observes that the ring systems increase in complexity with decreasing mean density. The mean densities are 1.33, 0.69, 1.29, and 1.64 respectively. The least dense planet, Saturn, is very large and would be expected to have a complex layered structure especially nearer the surface. The radii of the planets above are : 71,398 km, 60,300 km, 25,559 km, and 24,766 km respectively. Their densities are 1.3, 0.7, 1.3, and 1.6 respectively. Layered structures have been proposed for gaseous planets and studied for many years. The main oscillations of the gaseous planets apparently place the important satellites while the layer structure produces the rings. Note that the layers of the planet above the rocky core are likely much less dense and may not influence satellite orbits that drastically.

Calculations for SATURN

We use equation (1) to find a radius indicated by the first 3 significant satellites at 42,607 km. This leaves a 17,793 km possible active layer on top of a probable light core, which may also oscillate. Saturn may have had an early satellite around a small diameter rocky core but that orbit would likely not exist today since the mean density of Saturn is so small. Several satillites fit rather well if we increase the radius to 67,300 km from 60,268 km using equation (1) otherwise the satillites do not appear to be well organized probably because of the layering that apparently continued for some time. We will use the outer radii of the rings assuming that the inner parts result from oscillation of the same layer. Slow cooling also probably tended to randomize the satellites as the radius decreased with time. Note that Saturn’s surface gravity is 0.92 earth’s. We equate the sum of the periods of the rings to the thickness (magnitude in seconds) of the possible oscillating active outer layer. For simplicity and lack of knowledge of the composition of the layers and lack of knowledge of the real active layer thickness we equate the total period to the magnitude of the thickness of the possible active layers. The rings average distance from the planets surface is 113,247 km (indicating thick low frequency layers within the planet).

∑_n1/f_n=∑2(r_n-r₀)/s(1+r_n/r₀)/2=p_t=

1/s(2(14232)/((1.236)/2)+2(31732)/((1.527)/2)+2(57232)/((1.950)/2)+2(76332)/((2.267)/2)+2(79942)/((2.236)/2)+2(113532)/((2.884)/2)+2(419732)/(7.964)/2)=1/s(892552)=17793to obtain layer thicknesses of 2 x 17793 for s to be 25 m/s.

A 17,793 active portion of the planet apparently is correct but one has to double 17793 to get the equation to be correct and the surface velocity 25m/s.the signal must pass through a layer twice to represent a period. I suggest 25 m/s as the estimated surface velocity using twice the 17793 figure for the total period. The thickest active layer is 4208 km thick.


URANUS

In the case of Uranus it appears that we have many close together tiny satellites beginning just above the planet’s surface. Uranus is a unique planet with its axis of rotation nearly perpendicular to the other planets axes. Likely a catastrophic collision perhaps removed much of the hydrogen and helium and reducing the radius from near 70,000 km to 25559 km. Using equation 1 and the 5 massive middle satellites, equation 1 seems to suggest this. We can probably dismiss the other tiny satellites as just remnants of the collision. Likely most of the denser matter remains with the planet. The planet was also likely hotter when the main satellites were placed. We will use the present radius or the total planet as all-active and placing the rings.

Here it appears that all of the layers and the planet are oscillating. In the matter of the layers of the planet the velocities may be closer to the velocities in matter in the sun. In the atmosphere the velocities, probably closely follow the rule that the wave velocity is propotional to the reciprocal of the square root of the dencity of dark matter and thus would become much larger above the surface. We approximate this increase.

We notice that rings of Uranus overlap the satellites. Both the rings and most of the satellites cover the same range very closely. We use the range of a total of 25,559 km for the radius of the planet, for the layered portion of the planet. The oscillation frequency is just (average velocity above surface out to ring)/2(r-r₀). Now calculating for the surface velocity on Uranus from the ring distances above the planet’s surface: (I did not use faint dusty rings or inward extensions, or shepherded rings)

∑_n1/f_n=∑2(r_n-r₀)/s(1+r_n/r₀)/2=25559

1/s(4(15971)/(1+r₁/r₀)+4(16278)/(1+r₂/r₀)+4(16675)/(1+r₃/r₀)+4(17011)/
(1+r₄/r₀)+4(19159)/(1+r₅/r₀)+4(20102)/(1+r₆/r₀)+4(21617)/(1+r₇/r₀)+4(22068)/(1+r₈/r₀)+4(22741)/(1+r₉/r₀)+4(44341)/(1+r₁₀/r₀)+4(77441)/(1+r₁₁/r₀))= 25559
s=20.85 m/s for active layer thicknesses of 1872, 1908, 1936, 1959, 2101, 2159, 2247, 2272, 2309, 3162, and 3686 kilometers! Doubling the total period provides a surface velocity of 10.43 m/s, which may be a reasonable value for the surface velocity.

This velocity suggests that the surface density of dark matter depends on the planetary density with the least dense planet having the highest surface wave velocity and the least dense dark matter. The rings here are so close together there appears to be little inactive layering with little or no rocky core. The planets apparently collect their own dark matter without much regard for the sun. We estimate the velocities within the planet as with the other planets since compositions are unknown.

NEPTUNE

Using the orbit equation for Neptune we find different radii for different times of development of the planet. If we can depend on the first 5 satellites there are 4 layers in the satellite plus a top layer of 3619 km which may be related to a decrease in orbit radius due to added mass. We are not sure a satellite was added every time mass was added etc. The radius of Neptune is 27, 766 km. Apparently Neptune was forming at the same time as satellites were being placed. The relative mean density of Neptune is 1.64. The square root is 1.28 while the square root of the sun’s mean density is 1.19. In the calculations to find the layers that produce the rings of Neptune we will again a assume wave velocity of near 1or 2 m/s within the planet, which is likely incorrect. Different layers will likely have different velocities due to different compositions but at present we do not have that information. Note that Neptune is 17 times more massive than the earth. The mean velocity out to a ring, however, is the usual (v+v₀)/2. Neptune’s ring locations are:

1989NR3 @ 17134 km from Neptune’s surface

1989NR2 @ 26434

1989NR4 @28634-34234

1989NR1 @38164

The rocky core has an approximate radius of 11,000 km from an analysis of the satellites next to the planet (N=1 in equation 1). Its core likely makes Neptune the densest planet of the gaseous planets. Note that the average distance out to the rings from the planet’s surface is 28,992 km (or thin relatively high frequency oscillating layers within the planet).

Now lets get an idea of the surface velocity of the waves forming the rings above Neptune’s surface. 16,766 km is estimated to be, from satellite computations, the approximate thickness of the layers above the rocky core whose magnitude we call half the total period. We use the usual approximate calculation to arrive at a surface velocity s. Note that Neptune’s surface gravity is 112% of earth’s surface gravity.

∑1/f_n=1/s(2(17134)/((1+r₁/r₀)/2)
+2(26434)/((1+r₂/r₀)/2)+2(34234)/(1+r₃/r₀)+2(38164)/((1+r₄/r₀)/2)=13766
=1/s(4(17134)/1.692)+4(26434)/2.067+4(34234)/2.382+4(38164)/2.541=13766
s=15.2m/s

The low value may be a reasonable answer since Neptune has such a large
density. Using twice the calculation period gives a surface velocity of 7.6 m/s!

VARIABLE STARS

In star formation it is well known that before a star becomes a permanent feature that is usually throws of matter. I hypothesize that stars take on resonant size for dark matter oscillations. Thus the sun oscillates with the sunspot cycle. Sometimes a star just fails to attain a resonant size and is left with an extra layer of matter on top of a resonant star. This layer oscillates similarly to a gaseous planetary layer. The approximate period of oscillation would likely be equal to twice the layer thickness in meters assuming a dark matter wave velocity of 1 m/s. The period here would be equal to the period of the variable star with light being shut on and off accordingly.

THE APPARENT PERIODIC ORGANIZATION OF THE UNIVERSE.

Dark matter waves permeate the universe with standing waves. The lower the density of dark matter the farther apart the nodes in the system. Matter tends to collect on the nodes providing for walls of galaxies. I assume the farther away the walls of galaxies the farther apart they are and the faster they are spreading. If one goes far enough out one finds the dark matter thinning and the waves are accelerating to the next antinode location. A phenomenon related to this may explain dark energy.

CONCLUSIONS AND OBSERVATIONS

The calculated surface wave velocities are for Jupiter 10.1 m/s, Saturn 25 m/s, Uranus 10.4 m/s, and Neptune 7.6 m/s. Uranus apparently gave outstanding results because the rings are so close together. The whole thickness seems to be oscillating and the answer for the surface wave velocity seems reasonable without any modifications. Notice that the surface velocities don’t seem to depend much on the planet distances from the sun. This makes sense if we consider each planet a separate entity, which collects dark matter due to its own gravity.

In plants wave velocities are functions of the orientation of the plant part with respect to the gravitational field with vertical velocities the largest (Wagner 2008). The velocities increase in steps as the angle of the plant part with the horizontal increases to the vertical. Similar effects may be present around planets but we have only been dealing with vertical velocities so far. The shape of a plant seems to be determined by the ratio of the vertical/horizontal velocities since plant spacings apparently are determined by wavelengths. The horizontal velocity of waves traveling between plants appears to be near 25 m/s on earth with its air atmosphere (Wagner 1989, 2009). This velocity led me to believe the waves were traveling in another medium besides air. There are no other media around that support such velocities so dark matter was a candidate I could not ignore.

I attempted to find surface velocities directly so that I could calculate how much material above the rocky core was oscillating. In some cases the information might help determine the rocky core thickness. I wished to find actual thicknesses, which actual surface velocities would permit one to do. It appears, however, that all planets tend to collect and concentrate dark matter around them no matter what distance they are from the sun. The derived surface velocities may be somewhat larger for planets further from the sun indicating smaller dark matter densities. There is not as great a change, however, as would be indicated by the change in dark matter density due to the presence of the sun alone.

On the earth’s surface I studied wave systems other than plants. These also may be dark matter oscillators. For example I filled 12-inch diameter, level, plastic pipes half full with water and placed a thin layer of sawdust on the water surface and closed the pipe. After a few days the floating sawdust separated into what appeared to be a wave pattern with nodes and antinodes. Another experiment was slowly rotating a thin layer of granular material in glass tubes of differing diameters. The granular material produced a wave pattern with larger separations of nodes for larger diameter tubes (Wagner 1999b). I did the latter before I found out that physicists had made this phenomenon a field of physics! Another source of waves is an oscillating vacuum tube. I used a 6L6. Concentric nodes were observed going away from the tube. My oscillating frequency was in the hundreds of kilohertz with wavelengths of many meters. The concentric nodes were separated by a few centimeters no matter what the operating frequency perhaps indicating the excitation of dark matter. I searched many phenomena looking for possible manifestations of dark matter waves on earth.

An equation relating the dark matter density (d) to the dark matter wave velocity is as follows:

d=9.75x10⁷/v² Gev/cm³, where v is the wave velocity in m/s
See Wagner 2010.

The above relation gives the values for the surface dark matter densities for Jupiter, Saturn, Uranis, and Neptune.

I want to pose a question that I would like some one to answer since no one has ever discovered gravity waves except that they are supposedly emitted by pulsars. Could dark matter waves explain the so called emission of “gravity waves” from pulsars?

REFERENCES

(1) Wagner, O.E. (1989) W-waves and Plant Communication. Northw. Sci. 63:119-128 (1989) (Note velocity needs correction, due to a consistent timing error, from 4.9 m/s to 25 m/s)

(2) Wagner, O.E. Waves in Dark Matter. Physics Essays 12(1): 3-10 (1999a).

(3) Wagner, O.E. A basis for a unified theory for plant growth and development. Phys. Chem. Med. NMR, 31:109-129 (1999b).

(4)Frere, J.-M., Ling, F.-S., and Vertongen, G. Bound on the dark matter density in the solar system from planetary motions. Phys. Rev. D77, 083005 (2008).

(5) Wagner, O.E. Physics in whole plants. Physics Essays 21(2):151-157(2008).

(6) Wagner, O.E. 1/f Noise and Dark Matter Waves in Trees, Samples, and Air. Physics Essays.In press (2010).